A zero-coupon bond with a market-beta of 0.2 promises to pay $1,000 in the first year. However, it may default and pay nothing with probability 0.1%. If the risk-free rate is 5.3%, the equity premium is 6.5%, and the CAPM is correct, what would be the bond price today?________________ Carry out calculations to at least 4 decimal places. Enter percentages as whole numbers. Example: 3.03% should be entered as 3.03. Do not include commas or dollar signs in numerical answers.
Find the expected return on the bond using the Capital asset pricing | |||||||||
model. | |||||||||
Calculate the payoff from the bond using the probability given. | |||||||||
Using the payoff and the expected return you can calculate the price of the | |||||||||
bond. | |||||||||
The probability that the bond pays zero is .1%. | |||||||||
The probability that the bond pays 1000 is 99.9%. | |||||||||
Expected payoff = .999*1000 + .001*0 | |||||||||
Expected payoff = 999 | |||||||||
Under the Capital Asset pricing model | |||||||||
Rs = Rf + Beta*(Rm-Rf) | |||||||||
Rs is the expected return on the security | |||||||||
where Rf is the risk free rate that is .053, Rm - Rf = difference between the expected return on the market | |||||||||
portfolio and the riskfree rate. (Rm-Rf) = .065 | |||||||||
Beta = .2 | |||||||||
Rs = .053 + (.2*.065) | |||||||||
Rs = .066 | |||||||||
The expected return on the bond is .066. | |||||||||
Set up the cash flow for the bond and find the price. | |||||||||
Price of bond = present value of future cash flows. | |||||||||
Present Value = Future value/ ((1+r)^t) | |||||||||
where r is the interest rate that is 6.6% and t is the time period | |||||||||
Year | 1 | ||||||||
Cash flow | 999 | ||||||||
Present value | 937.15 | ||||||||
The price of the bond is 937.15. |
A zero-coupon bond with a market-beta of 0.2 promises to pay $1,000 in the first year....
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